Data analysis techniques are reviewed and extended for the measurement of the Stokes vector of partially or completely polarized radiation by the rotating quarter-wave method. It is shown that the conventional technique, based on the Fourier analysis of the recorded signal, can be efficiently replaced by a weighted least-squares best fit, so that the different accuracy of the measured data can be taken into account to calculate the measurement errors of the Stokes vector elements. Measurement errors for the polarization index P and for the azimuth and ellipticity angles ψ and χ of the radiation are also calculated by propagation error theory. For those cases in which the above technique gives a nonphysical Stokes vector (i.e., with a polarization degree of P > 1) a constrained least-squares best fit is introduced, and it is shown that in this way a Stokes vector with P = 1 (rather than P ≤ 1) is always obtained. In addition an analysis technique useful to remove from the measured data systematic errors due to initial misalignment of the rotating quarter-wave axis is described. Examples of experimental Stokes vectors obtained by the above tech- niques during the characterization of components for a far-infrared polarimeter at λ = 118.8 μm for applications in plasma diagnostics are presented and discussed. Finally the problem of the experimental determination of physically consistent Mueller matrices (i.e., of Mueller matrices for which the transformed Stokes vector has always P ≤ 1) is discussed, and it is shown that for simple Mueller matrices of the ABCD type, whose elements can be determined by the measurement of a single Stokes vector, the imposed P ≤ 1 constraint gives a sufficient condition for physical consistency. On the other hand, the same constraint, when imposed to the set of four basic Stokes vectors conventionally measured for the determi- nation of a full 16-element Mueller matrix, gives only a necessary but not a sufficient condition.
Data analysis for a rotating quarter-wave, far-infrared Stokes polarimeter
GIUDICOTTI, LEONARDO
Writing – Original Draft Preparation
;BROMBIN, MATTEO
Membro del Collaboration Group
2007
Abstract
Data analysis techniques are reviewed and extended for the measurement of the Stokes vector of partially or completely polarized radiation by the rotating quarter-wave method. It is shown that the conventional technique, based on the Fourier analysis of the recorded signal, can be efficiently replaced by a weighted least-squares best fit, so that the different accuracy of the measured data can be taken into account to calculate the measurement errors of the Stokes vector elements. Measurement errors for the polarization index P and for the azimuth and ellipticity angles ψ and χ of the radiation are also calculated by propagation error theory. For those cases in which the above technique gives a nonphysical Stokes vector (i.e., with a polarization degree of P > 1) a constrained least-squares best fit is introduced, and it is shown that in this way a Stokes vector with P = 1 (rather than P ≤ 1) is always obtained. In addition an analysis technique useful to remove from the measured data systematic errors due to initial misalignment of the rotating quarter-wave axis is described. Examples of experimental Stokes vectors obtained by the above tech- niques during the characterization of components for a far-infrared polarimeter at λ = 118.8 μm for applications in plasma diagnostics are presented and discussed. Finally the problem of the experimental determination of physically consistent Mueller matrices (i.e., of Mueller matrices for which the transformed Stokes vector has always P ≤ 1) is discussed, and it is shown that for simple Mueller matrices of the ABCD type, whose elements can be determined by the measurement of a single Stokes vector, the imposed P ≤ 1 constraint gives a sufficient condition for physical consistency. On the other hand, the same constraint, when imposed to the set of four basic Stokes vectors conventionally measured for the determi- nation of a full 16-element Mueller matrix, gives only a necessary but not a sufficient condition.
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